We have prepared nanometer-sized gold clusters on alkanethiol [CH3 (CH2) n-1 SH, abbreviated as Cn] self-assembled monolayers (SAMs) on Au (111) substrates by thermal evaporation. Typically, the Au clusters are one atomic layer thick and plate-like, with a diameter of～2-10nm. While most of the Au clusters are found at the SAM/Au (111) interface, a fraction of the clusters reside on top of the SAMs as evidenced by the existence of the Coulomb blockade and Coulomb staircase in the scanning tunneling spectroscopy. Using scanning tunneling microscopy under ambient conditions, we also investigated the stability of the gold clusters at the SAM/Au (111) interface. For a given nominal coverage of Au, the gold clusters on C7 are larger and diffuse faster than those on C10 and C18.